A sonometer wire is in unison with a tuning fork, when it is stretched by weight w and corresponding resonating length is L 1 . If the weight reduced to w 4 , the corresponding resonating length becomes L 2 . The ratio L 1 L 2

Step-by-step solution

When sonometer is stretched by weight w (tension), then frequency of vibration in the string v = 1 2 l T m v = 1 2 L 1 w m … (i) where, L 1 is the resonating length and m is mass per unit length of the string. Similarly, when weight reduces to w 4 and Resonating lengths is L 2 , then v = 1 2 L 2 w 4 m ⇒ v = 1 4 L 2 w m …(ii) From Eqs. (i) and (ii), we have 1 2 L 1 w m × 1 4 L 2 w m ⇒ L 1 = 2 L 2 ∴ L 1 L 2 = 2 ∴ L 1 : L 2 = 2 : 1